A rectangular prism has length 444, width 476, and height 14. Find its volume.

Step-by-step solution

1. 1

   Start from the definition of volume for a box. A rectangular prism is filled by unit cubes arranged in a $444\times476$ rectangle, stacked $14$ layers deep, so the count is simply the product of the three edge lengths:

   $V=\text{length}\times\text{width}\times\text{height}=444\times476\times14$

2. 2

   Multiply two factors first so only one large product is in play at a time. Take $444\times476$ and split $476$ into $400+76$ — partial products keep every intermediate number small enough to verify:

   $444\times400=177{,}600,\qquad 444\times76=33{,}744$

   $444\times476=177{,}600+33{,}744=211{,}344$

3. 3

   Multiply the running product by the height using the same split. Write $14=10+4$:

   $211{,}344\times10=2{,}113{,}440,\qquad 211{,}344\times4=845{,}376$

   $211{,}344\times14=2{,}113{,}440+845{,}376=2{,}958{,}816$

4. 4

   Sanity-check the magnitude before trusting the digits. Round to $440\times480\times14=2{,}956{,}800$. The exact answer $2{,}958{,}816$ sits within $0.1\%$ of that estimate, so no digit has been dropped or misplaced.

5. 5

   State the volume with units. Because the three edges were given in the same length unit, the volume comes out in cubic units of that unit:

   $V=2{,}958{,}816\text{ cubic units}$